Okay, so a small update on my #OwnMailServer:
I've just managed to send and receive my first mail! And I can connect to my new inbox via the webmail interface, and also via Thunderbird (imap).
Apart from running the standard dockerized version of #MailCow, I had to do two things:
Serve the MailCow web interface to the internet (ports 80 and 443). Because I'm hosting various websites on those ports, I used Nginx to forward the MailCow traffic to the relevant port on a local machine.